A: Yes, but keep in mind cover photos are generally higher resolution than profile pics by default. The same URL manipulation works.
Most "viewer" tools operate using one of two methods: facebook full link size profile picture viewer
If you see a blue default silhouette, it means the user has a temporary avatar (like a character from a game) or the ID is wrong. For most real users, this method pulls the original upload. A: Yes, but keep in mind cover photos
Navigate to the profile and long-press the picture to "Open image in new tab." This version is often uncropped compared to the app. : facebook full link size profile picture viewer